Question: Simplify the following expression: $ n = \dfrac{-1}{7} - \dfrac{8y - 7}{-10} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10}{-10}$ $ \dfrac{-1}{7} \times \dfrac{-10}{-10} = \dfrac{10}{-70} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{8y - 7}{-10} \times \dfrac{7}{7} = \dfrac{56y - 49}{-70} $ Therefore $ n = \dfrac{10}{-70} - \dfrac{56y - 49}{-70} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{10 - (56y - 49) }{-70} $ Distribute the negative sign: $n = \dfrac{10 - 56y + 49}{-70}$ $n = \dfrac{-56y + 59}{-70}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{56y - 59}{70}$